Your words were "My current counsellor says it's the ones with trauma that make the best counsellors."
This is a lie.
He lied to you either deliberately or because he is completely lacking insight. And he is in a position of trust and power around vulnerable people, while making up nonsense narratives like this. That is very concerning indeed.
Traumatised people absolutely definitively do NOT make the best counsellors.
Those with trauma often believe it to be resolved and then discover it is absolutely not resolved when they are triggered. Triggering happens regularly when working with mentally ill people. Only emotionally resilient, stable people are able to handle the extreme emotional pressures of counselling/the therapeutic role
Trauma can cause countertransference, where your own pain gets triggered and projected onto clients. Trauma sufferers often lack sufficient emotional boundaries (as you seem to) leading to ove identification, enmeshment and blurred roles.
Those who have experienced trauma often unintentionally re-enact trauma dynamics (rescuer/victim/persecutor) with vulnerable clients.
Those with trauma often struggle with self regulation increasing the risk of harmful boundary violations, emotional dumping (as you have pointed out you engage in) and destabilising responses.
Personal trauma impairs the objectivity, containment, and safety required to hold space for others without causing harm.
The very best counsellors/therapists have strong ethical boundaries, self awareness and emotional resilience. The very qualities you appear to be lacking, and which many who have experienced trauma also lack.
Sometimes those who have experienced trauma can indeed be good counsellors, psychotherapists, psychologists etc.
But most of the time people who have been traumatised cannot deal with the emotional requirements of counselling/psychotherapy.
Trauma does not ever make you stronger or more resilient. Not. Ever. Trauma is cumulative. Every genuine trauma a peson endures affects them more strongly.
Trauma can sometimes be satisfactorily resolved and if the underlying personality is strong and resilient enough that person can work in a therapeutic role.
So either you are incorrect about what he said or he has a startling and very worrying lack of understanding about the counselling role and emotional requirements for that role and this makes him a danger to be around vulnerable people.
People with mental health challenges are often drawn to psychotherapeutic roles, which is understandable. Sometimes they do make good counsellors/therapists - eventually long after their own trauma and mental health issues have been resolved, dealt with and are stable.
But your words here indicate that you are not even close to being mentally healthy, stable and resilient enough to be a counsellor.